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They also say that they give more weight to links from sites that are 'further away' from the site being linked to, I assume that this is also done via IP address to filter out hundreds of links from sites hosted on the same server.
My question is, which IP address(es) do Google use?
The nameserver (listed on the whois) is one IP address.
The IP address of the server where the site is hosted is another.
The IP address that you can type in to reach the site is another possibility.
Has anyone done any research into how Google views IP addresses and how they are used?
I assume otherwise. There really isn't a very strong correlation between IP address adjacency and site relatedness -- there's basically just one level of clustering.
My assumption is that Google measures "distance" from page A to page B as "the inverse of the probability that starting from page A, a random spider would arrive at page B."
That is, reciprocated links are much less valuable than less obviously artificial link patterns.
There are other possible approaches, but anecdotal evidence is that many large multi-unrelated-IP clusters of fraternal doorway sites have recently been "withering on the vine"; my assumption would readily account for this, and yours wouldn't.